Question

If Θ is between 0° and 90° and tanθ = 7/8 find cosθ

Answer 1

Since 0° < θ < 90°, you know that cos(θ) > 0.

Recall that

1 + tan²(θ) = sec²(θ)

and also that

sec(θ) = 1/cos(θ)

So if cos(θ) > 0, we also have 1/cos(θ) = sec(θ) > 0.

Then

sec(θ) = + √(1 + tan²(θ))

sec(θ) = √(1 + (7/8)²)

sec(θ) = √113 / 8

so that

cos(θ) = 1 / (√113 / 8) = 8 / √113